A050700 -id:A050700 - cp's OEIS frontend

A050699 Nonprime numbers n such that n and n-reversed (<> n and no leading zeros) have the same number of prime factors (counted with multiplicity).

15, 26, 39, 49, 51, 58, 62, 85, 93, 94, 115, 117, 122, 123, 126, 129, 143, 147, 155, 158, 159, 165, 169, 177, 178, 183, 185, 187, 203, 205, 221, 225, 226, 244, 246, 265, 285, 286, 289, 294, 302, 314, 315, 319, 321, 326, 327, 329, 335, 338, 339, 341, 355, 366

Offset: 1

Patrick De Geest, Aug 15 1999

			E.g., 321 = 3*107 and 123 = 3*41 -> both 321 and 123 have two prime factors.

Nathaniel Johnston, Table of n, a(n) for n = 1..10000

Cf. A050700, A050701, A050702, A006567, A097393, A109018-A109031.

with(numtheory): read(transforms): for n from 12 to 366 do r:=digrev(n): if(not isprime(n) and not n=r and not n mod 10 = 0 and bigomega(n)=bigomega(r))then printf("%d, ", n); fi: od: # Nathaniel Johnston, Jun 23 2011

nrnQ[n_]:=Module[{idn=IntegerDigits[n],rev},rev=Reverse[idn];!PrimeQ[n] &&First[rev]!=0&&idn!=rev&&PrimeOmega[n]==PrimeOmega[FromDigits[rev]]]; Select[Range[400],nrnQ] (* Harvey P. Dale, Jun 23 2011 *)

Definition clarified by Harvey P. Dale, Jun 23 2011

A050701 If composite k and its reverse are different and have same number of prime factors, then the larger of them is a term of the sequence.

Original entry on oeis.org

51, 62, 85, 93, 94, 221, 302, 321, 341, 381, 413, 442, 492, 493, 502, 511, 513, 514, 522, 524, 533, 534, 551, 553, 561, 562, 574, 581, 582, 604, 605, 621, 622, 623, 642, 663, 682, 685, 705, 711, 723, 734, 741, 766, 771, 781, 794, 805, 814, 817

Offset: 1

Patrick De Geest, Aug 15 1999

			a(n)=341 -> reverse(a(n)) = 143 gives the pair (143,341) of which only the larger value 341 is retained.

Cf. A004086, A050699, A050700.

rev[n_]:=FromDigits[Reverse[IntegerDigits[n]]]; Select[Range[825],!PrimeQ[#]&&PrimeOmega[#]==PrimeOmega[x=rev[#]]&&#>x&] (* Jayanta Basu, May 31 2013 *)

isok(m) = my(k=fromdigits(Vecrev(digits(m)))); (m%10) && !isprime(m) && (m>k) && (bigomega(k) == bigomega(m)); \\ Michel Marcus, Aug 18 2021

Revised by Editors of OEIS, Oct 19 2019

Incorrect 394 and 523 removed and name clarified by Sean A. Irvine, Aug 17 2021

A373731 Semiprimes k such that the digit reversal of k is a semiprime > k.

Original entry on oeis.org

15, 26, 39, 49, 58, 115, 122, 123, 129, 143, 155, 158, 159, 169, 177, 178, 183, 185, 187, 203, 205, 226, 265, 289, 314, 319, 326, 327, 329, 335, 339, 355, 394, 398, 415, 437, 497, 538, 559, 586, 589, 629, 667, 718, 899, 1006, 1011, 1027, 1041, 1043, 1046, 1047, 1057, 1059, 1067, 1079, 1115, 1119

Offset: 1

Zak Seidov and Robert Israel, Jun 17 2024

			a(3) = 39 is a term because 39 = 3*13 is a semiprime, its reversal 93 = 3*31 is a semiprime, and 93 > 39.

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A001358, A004086, A050700, A097393.

rev:= proc(n) local L,i;
  L:= convert(n,base,10);
  add(L[-i]*10^(i-1),i=1..nops(L))
end proc:
filter:= proc(n) local r;
  r:= rev(n);
  r > n and numtheory:-bigomega(n) = 2 and numtheory:-bigomega(r) = 2
end proc:
select(filter, [$1..2000]);

s = {}; Do[fd = FromDigits[Reverse[IntegerDigits[k]]]; If[{2, 2} ==PrimeOmega[{fd, k}] && fd > k, AppendTo[s, k]], {k, 1000}]; s

cp's OEIS Frontend

A050699 Nonprime numbers n such that n and n-reversed (<> n and no leading zeros) have the same number of prime factors (counted with multiplicity).

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Maple

Mathematica

Extensions

A050701 If composite k and its reverse are different and have same number of prime factors, then the larger of them is a term of the sequence.

Views

Author

Keywords

Examples

Crossrefs

Programs

Mathematica

PARI

Extensions

A373731 Semiprimes k such that the digit reversal of k is a semiprime > k.

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Maple

Mathematica